Instead of using the compound interest formula, we use this formula: A= p e rt. In this formula, A is the amount that accumulates, p is the principal, r is the interest rate as a decimal, and t is the time in years. The number e is a base that plays an important role in mathematics and is used to determine the solution to many application problems. Base e is called Euler's constant or Euler's number. We will encounter Euler's constant again in Unit 3 and we'll also learn more about Leonhard Euler in Unit 4 (Graph Theory). NOTE: Euler is pronounced OY-ler. (reference: Leonhard Euler biography) Your calculator may have a base e key (usually a 2nd function above the ln x key) or you can approximate e as 2.7183. In this discussion, we'll compare different compounding periods with continuous compounding to see if there is a significant difference in the amount that accumulates. Here's an example. Let's say we are investing $5000 for 14 years. We'll compare annual, quarterly and monthly compounding at 3% with continuous compounding. See this short video Unit 2 Discussion Video and this handout for details of the calculations: Unit 2 Discussion Calculations Compounding Accumulated Amount Annual $7562.95 Quarterly $7597,89 Monthly $7605.82 Continuous $7609.81 Continuous compounding over the 14 year period at a rate of 3% provided an additional $46.86 in accrued interest when compared to annual compounding. For this discussion, you will post at least twice - 1) an initial post, and then 2) a reply to a classmate. For your initial post Let's assume we have $10,000 to invest. Select one of the following investment options: Invest at 6% for 10 years Invest at 6% for 20 years Invest at 8% for 10 years Invest at 8% for 20 years For the investment option you selected answer the following questions: Find the amount that accumulates if the interest is compounded annually. Find the amount that accumulates if the interested is compounded continuously. Considering the amounts calculated for question 1 and 2, which had a better outcome? By how much?